A top U.S. general just said 4,000 American troops are in Syria. The Pentagon says there are only 500.

A senior U.S. military commander said Tuesday that 4,000 American troops are on the ground in Syria, a figure far greater than the 503 personnel the Trump administration says are deployed there.

Army Maj. Gen. James B. Jarrard, who heads the U.S.-led Special Operations task force targeting the Islamic State in Syria and Iraq, offered the surprising figure while briefing Pentagon-based reporters via satellite from Baghdad.

When asked to confirm the 4,000 figure, Jarrard appeared to be caught off guard. He then apologized and said the number is about 500. Eric Pahon, a Pentagon spokesman facilitating the briefing, interjected moments later, insisting the number is just 503.

Yet it’s long been an open secret that the Pentagon has far more personnel involved in operations against the Islamic State, also known as ISIS, than its publicly disclosed figures. Hundreds of additional American forces — including Special Operations troops, forward air controllers and artillery crews — moved into Syria to back up allied local forces as they prepared to assault Raqqa, which was the Islamic State’s self-declared capital until its fall this month.

Earlier this year, teams of Army Rangers were rushed to Manbij for a mission the Pentagon called “reassurance and deterrence,” which was intended to maintain peace between Syrian Kurdish forces who liberated the city and armed groups loyal to neighboring Turkey. U.S. commanders also routinely send attack helicopters into Syria and leave them there, sometimes for days at a time.

The Trump administration says there are 5,262 U.S. troops supporting war efforts in Iraq, though the number is believed to be much higher.

“It’s widely acknowledged there are more than 503 in Syria and 5,200 in Iraq,” Pahon told The Post. “These are our force management level numbers. They don’t include temporary forces.”

A U.S. Marine guides an M777A2 Howitzer to a firing position May 14 in Syria. (Sgt. Matthew Callahan/U.S. Marine Corps)

Jennifer Cafarella, a Syria expert at the Institute for the Study of War, said sensitivity over U.S. troop levels in Syria and Iraq dates to the Obama administration, which was determined to fight the Islamic State with a minimal American presence on the ground.

“President Obama,” she said, “was forced to repeatedly scale up the U.S. role after it became clear that his initial strategy to partner with local forces could not generate the necessary outcomes without greater U.S. involvement. Whether or not Major General Jarrard’s statement was accurate, the U.S was certainly drawn deeper into Iraq and Syria than it seems was originally planned. This troop creep reflects flaws in the design of U.S. strategy against ISIS that U.S. policymakers continue to fail to recognize.”

These are not the only countries where the Pentagon appears to have manipulated deployment numbers. As the Wall Street Journal revealed in August, there are about 3,000 more troops on the ground in Afghanistan than the administration’s official tally showed.

The Pentagon has faced growing pressure from Congress to be more transparent about the scope of its activities overseas, not only in the Middle East but also throughout Africa and pockets of Southeast Asia. Defense Secretary Jim Mattis has promised to comply, but Jarrard’s statement Monday is likely to raise deeper suspicion among those who’ve renewed scrutiny of the military’s sprawling counterterrorism operations since the deaths of four American soldiers Oct. 4 in Niger.

Some lawmakers were taken aback by the size and scope of U.S. combat forces deployed throughout Africa. About 800 Americans are based in Niger to run counterterrorism operations and to train and advise local troops, and hundreds more U.S. forces are in other African countries.

Mattis was summoned to Capitol Hill along with Secretary of State Rex Tillerson on Monday for a hearing over whether to update the laws that provide authority to fight terrorist groups and detain militants on multiple continents. They presented a unified front, saying that is unnecessary. Both indicated the administration is concerned about new laws inhibiting the military’s ability to target terrorists anywhere in the world.